In the following topology, network S is multi-homed to four providers, i.e., P1, P2, P3 and P4, where P1, P2 and P3 are customers of a common provider P while P4 is a customer. Now suppose D is the destination of interest.

(a) What are the possible routing paths to D that S can have in its BGP routing table?

(b) Suppose S maintains all possible routing paths in its BGP routing table, and S prefers the paths going through the provider P (say, due to lower cost). Now suppose P is broken, what can P1, P2 and P3 announce (withdraw) to S via BGP updates?

(c) Suppose only the announcement from P1 arrives at S, while the announcements from P2 and P3 are lost. How can S find a working path to D? (show the path exploration process of S)

(d) If you think the above path exploration process is undesirable, how can you suggest to improve it? (you can modify the BGP routing protocol in any reasonable way)